The following concept from the seminal paper [1]} is very useful. A vertex \( u \in N_G(v)\)  is a maximal neighbor of \(v\)  if all neighbors of \(v\)  (and \(v\)  itself) are in \(N_G[u]\) . That is, \(u\)  is a maximal neighbor of \(v\)  if \(u\)  is adjacent to all neighbors of \(v\) . The next Lemma REF  implicitly follows from [1]}.
